Ok, theatre strategy. I like to start by looking at what tickets have been available recently for discount at the TKTS booth. For instance, today's offerings at the TKTS booth include several of Time Out's recommendations.
Although it's kinda cheesy, one of the gang wants to see Fame, which I've found generally available at TKTS.
Musicals seem to have enough energy that you don't doze off in the middle from jet lag. So, Les Miz and Phantom sound pretty good.
Epitaph for George Dillon is billed as a comedy, but, when I saw it in October, it certainly wasn't a laugh a minute. Pretty adult, but the redeeming factor here is Joseph Fiennes in a lead role.
Last, Lion King, which I've been warned off of, but I don't think we'll be going to New York anytime soon to see it, so perhaps this is the right time and place.